Bošković, Ruđer Josip, Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium

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              <pb o="102" file="0154" n="154" rhead="THEORIÆ"/>
            ad intervallum æquale dimidiæ amplitudini unius e quinque
              <lb/>
            iis arcubus, uti uni G I, vel I L; </s>
            <s xml:space="preserve">in fig. </s>
            <s xml:space="preserve">29 ad intervallum
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            æquale integræ ipſi amplitudini; </s>
            <s xml:space="preserve">in fig. </s>
            <s xml:space="preserve">30 ad intervallum æ-
              <lb/>
            quale duplæ ſint autem puncta L, N in omnibus hiſce figu-
              <lb/>
            ris eadem, & </s>
            <s xml:space="preserve">
              <gap/>
            uæratur, quæ futura ſit vis in quovis puncto
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            g intervalli LN in hiſce tribus poſitionibus punctorum B' B.</s>
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          <p>
            <s xml:space="preserve">221. </s>
            <s xml:space="preserve">Si in Fig. </s>
            <s xml:space="preserve">27 capiantur hinc, & </s>
            <s xml:space="preserve">inde ab ipſo g inter-
              <lb/>
              <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">Determinatio
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              vis compoſitæ
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              in iiſdem.</note>
            valla æqualia intervallis AB', AB reliquarum trium figura-
              <lb/>
            rum ita, ut g e, g i reſpondeant figuræ 28; </s>
            <s xml:space="preserve">g c, g m figuræ
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            29; </s>
            <s xml:space="preserve">g a, g o figuræ 30; </s>
            <s xml:space="preserve">patet, intervallum e i fore æquale
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            amplitudini L N, adeoque L c, N i æquales fore dempto com-
              <lb/>
            muni L i, ſed puncta e, i debere cadere ſub arcus proximos
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            directionum contrariarum; </s>
            <s xml:space="preserve">ob arcuum vero æqualitatem fore æ-
              <lb/>
            qualem vim e f vi contrariæ i l, adeoque in fig. </s>
            <s xml:space="preserve">28 vim ab u-
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            traque compoſitam, reſpondentem puncto g, fore nullam. </s>
            <s xml:space="preserve">At
              <lb/>
            quoniam g c, g m integræ amplitudini æquantur; </s>
            <s xml:space="preserve">cadent puncta
              <lb/>
            c, m ſub arcus IK L, NOP, conformes etiam directione inter
              <lb/>
            ſe, ſed directionis contrariæ reſpectu arcus LM N, eruntque
              <lb/>
            æquales m N, c I ipſi g L, adeoque attractiones m n, c d, & </s>
            <s xml:space="preserve">
              <lb/>
            repulſioni g b æquales, & </s>
            <s xml:space="preserve">inter ſe; </s>
            <s xml:space="preserve">ac idcirco in figura 29 ha-
              <lb/>
            bebitur vis attractiva g b compoſita ex iis binis dupla repulſi-
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            væ figuræ 27. </s>
            <s xml:space="preserve">Demum cum g a, g o ſint æquales duplæ ampli-
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            tudini, cadent puncta a, o ſub arcus GH I, PQR conformis
              <lb/>
            directionis inter ſe, & </s>
            <s xml:space="preserve">cum arcu LM N, eruntque pariter bi-
              <lb/>
            næ repulſiones a b, o p æquales repulſioni g b, & </s>
            <s xml:space="preserve">inter ſe.
              <lb/>
            </s>
            <s xml:space="preserve">Quare vis ex iis compoſita pro fig. </s>
            <s xml:space="preserve">30 erit repulſio g b dupla
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            repulſionis g b figuræ 27, & </s>
            <s xml:space="preserve">æqualis attractioni figuræ 29.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">222. </s>
            <s xml:space="preserve">Inde igitur jam patet, loci geometrici exprimentis
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              <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">In alia diſpo-
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              ſitione vim in
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              tractu continuo
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              fore nullam, in
                <lb/>
              alia attractio
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              nem, in alia re-
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              pulſionem, ma
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              nente diſtantia:
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              uſus in Phy-
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              fica ſummus.</note>
            vim compoſitam, qua bina puncta B', B agunt in tertium,
              <lb/>
            partem, quæ reſpondet intervallo eidem L N, fore in prima
              <lb/>
            e tribus eorum poſitionibus propoſitis ipſum axem L N, in
              <lb/>
            ſecunda arcum attractivum LM N, in tertia repulſivum,
              <lb/>
            utroque recedente ab axe ubique duplo plus, quam in fig. </s>
            <s xml:space="preserve">27;
              <lb/>
            </s>
            <s xml:space="preserve">ac pro quovis ſitu puncti g in toto intervallo LN in primo
              <lb/>
            e tribus caſibus fore prorſus nullam, in ſecundo fore attractio-
              <lb/>
            nem, in tertio repulſionem æqualem ei, quam bina puncta
              <lb/>
            B', B exercerent in tertium punctum ſitum in g, ſi colloca-
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            rentur ſimul in A, licet in omnibus hiſce caſibus diſtantia
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            puncti ejuſdem g a medio ſyſtematis eorundem duorum pun-
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            ctorum, ſive a centro particulæ conſtantis iis duobus punctis
              <lb/>
            ſit omnino eadem. </s>
            <s xml:space="preserve">Poſſunt autem in omnibus hiſce caſibus
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            puncta B', B eſſe ſimul in arctiſſimis limitibus cohæſionis inter
              <lb/>
            ſe, adeoque particulam quandam conſtantis poſitionis conſtitue-
              <lb/>
            re. </s>
            <s xml:space="preserve">Æqualitas ejuſmodi accurata inter arcus, & </s>
            <s xml:space="preserve">amplitudines,
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            ac limitum diſtantias in figura 1 non dabitur uſpiam; </s>
            <s xml:space="preserve">cum nul-
              <lb/>
            lus arcus curvæ derivatæ utique continuæ, deductæ nimirum
              <lb/>
            certa lege a curva continua, poſſit congruere accurate cum re-
              <lb/>
            cta; </s>
            <s xml:space="preserve">at poterunt ea omnia ad æqualitatem accedere, </s>
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